We follow a technique used by Gamburd [1]} and by Chmutov and Pittel [2]}. In their papers, they use a bound on the total variation distance due to Diaconis and Shahshahani [3]}. They combine this with a bound on character values of the Symmetric group. The character bound due to Larsen and Shalev [4]} will give us some kind of asymptotic form of Theorem REF . However the character values in our application are simpler than those in the aforementioned papers, so we do not need to apply such general machinery. It will also be convenient to have a more concrete character bound. We will therefore start by estimating the character values we need with a simple bound, with no asymptotic notation.
